December 13, 2025
What is a system of equations?A system of equations is a set of two or more equations that must be true at the same time, usually involving the same variables. Each equation is a condition, but the system asks for values that satisfy all conditions together. For two-variable linear systems, you can picture each equation as a line on a graph, and the solution is where the lines intersect. Depending on how the equations relate, a system can have one solution (lines cross once), no solution (lines are parallel), or infinitely many solutions (the equations describe the same line). Systems of equations matter because real problems rarely have just one constraint, and they show up in business, engineering, science, and computing whenever you need a single set of values that fits multiple rules.